Problem: Solve for $x$ and $y$ using elimination. ${-3x-5y = -53}$ ${5x-2y = -15}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $-5$ ${-6x-10y = -106}$ $-25x+10y = 75$ Add the top and bottom equations together. $-31x = -31$ $\dfrac{-31x}{{-31}} = \dfrac{-31}{{-31}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-3x-5y = -53}\thinspace$ to find $y$ ${-3}{(1)}{ - 5y = -53}$ $-3-5y = -53$ $-3{+3} - 5y = -53{+3}$ $-5y = -50$ $\dfrac{-5y}{{-5}} = \dfrac{-50}{{-5}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {5x-2y = -15}\thinspace$ and get the same answer for $y$ : ${5}{(1)}{ - 2y = -15}$ ${y = 10}$